Answered

Find expert answers and community support for all your questions on IDNLearn.com. Our platform is designed to provide trustworthy and thorough answers to any questions you may have.

a sphere of mass 40kg is attracted by a sphere of mass 80kg with aforce equal to 1/4th of a milligram weight when their centres are 30cm apart . calculate value of G

Sagot :

Jacob193idn

Answer:

Approximately [tex]6.898\times 10^{-11}\; {\rm N\cdot m^{2}\cdot kg^{-2}}[/tex].

Explanation:

Between two spherical mass of uniform density, the gravitational force [tex]F[/tex] would be:

[tex]\displaystyle F = \frac{G\, m_{1}\, m_{2}}{r^{2}}[/tex],

Where:

  • [tex]G[/tex] is the gravitational constant,
  • [tex]m_{1}[/tex] and [tex]m_{2}[/tex] are the mass of the two spheres, and
  • [tex]r[/tex] is the distance between the center of the two spheres.

In this question, [tex]F[/tex], [tex]m_{1}[/tex], [tex]m_{2}[/tex], and [tex]r[/tex] are given. To find the value of [tex]G[/tex], rearrange the equation above:

[tex]\displaystyle G = \frac{F\, r^{2}}{m_{1}\, m_{2}}[/tex].

Before substituting in the values, make sure all quantities that are involved are in standard units.

  • Force should be in Newtons. The question stated the value of [tex]F[/tex] in terms of milligram ([tex]1\; {\rm mg} = 10^{-3}\; {\rm g} = 10^{-6}\; {\rm kg}[/tex]) weight. Assuming that [tex]g = 9.81\; {\rm N\cdot kg^{-1}}[/tex]:
    [tex]\begin{aligned} F &= m\, g \\ &= (0.25 \times 10^{-6}\; {\rm kg}) \times (9.81\; {\rm N\cdot kg^{-1}}) \\ &= 2.7025 \times 10^{-6}\; {\rm N}\end{aligned}[/tex].
  • Mass should be measured in kilograms.
  • Distance should be measured in meters:
    [tex]r = 30\; {\rm cm} = 0.30\; {\rm m}[/tex].

Substitute the values into the expression for [tex]G[/tex]:

[tex]\begin{aligned} G &= \frac{F\, r^{2}}{m_{1}\, m_{2}} \\ &= \frac{(2.7025\times 10^{-6}\; {\rm N})\, (0.30\; {\rm m})^{2}}{(40\; {\rm kg})\, (80\; {\rm kg})} \\ &\approx 6.898 \times 10^{-11}\; {\rm N\cdot m^{2}\cdot kg^{-2}}\end{aligned}[/tex].

(The reference value of the gravitational constant is approximately [tex]6.7 \times 10^{-11}\; {\rm N\cdot m^{2}\cdot kg^{-2}}[/tex].)

We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Trust IDNLearn.com for all your queries. We appreciate your visit and hope to assist you again soon.